2h^2-h-78=0

Solution for 2h^2-h-78=0 equation:

Simplifying
2h2 + -1h + -78 = 0

Reorder the terms:
-78 + -1h + 2h2 = 0

Solving
-78 + -1h + 2h2 = 0

Solving for variable 'h'.

Factor a trinomial.
(-6 + -1h)(13 + -2h) = 0

Subproblem 1
Set the factor '(-6 + -1h)' equal to zero and attempt to solve:

Simplifying
-6 + -1h = 0

Solving
-6 + -1h = 0

Move all terms containing h to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1h = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1h = 0 + 6
-1h = 0 + 6

Combine like terms: 0 + 6 = 6
-1h = 6

Divide each side by '-1'.
h = -6

Simplifying
h = -6
Subproblem 2
Set the factor '(13 + -2h)' equal to zero and attempt to solve:

Simplifying
13 + -2h = 0

Solving
13 + -2h = 0

Move all terms containing h to the left, all other terms to the right.

Add '-13' to each side of the equation.
13 + -13 + -2h = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2h = 0 + -13
-2h = 0 + -13

Combine like terms: 0 + -13 = -13
-2h = -13

Divide each side by '-2'.
h = 6.5

Simplifying
h = 6.5
Solution
h = {-6, 6.5}